We employ advanced physical and mathematical methods to understand the biophysics of complex cellular processes. A major emphasis has been on the biogenesis of coated vesicles involved in clathrin mediated endocytosis (CME) and other intracellular transport processes. CME is the principal pathway for the regulation of receptors, and internalization of certain nutrients and signaling molecules, at the plasma membrane of eukaryotic cells. Defects in CME can lead to metabolic disorders, aberrant signaling related to various cancers, and neurological disorders. The process is central to several emerging biotechnological processes, including targeted drug delivery and gene transfer. The early stage of receptor mediated endocytosis involves the formation of transient structures known as clathrin coated pits (CCPs). This process depends on the detailed energetics of protein binding and associated membrane transformations. The CCPs either mature into clathrin coated vesicles (CCVs) or regress and vanish from the cell surface. During CCP formation, clathrin and several other proteins assemble to form a coat on the cytoplasmic side of the outer cell membrane. We have developed a simple physical model for CCP dynamics and have carried out Monte Carlo simulations to investigate the time development of CCP size and, by fitting the results of the simulations to experimental data, we have been able to estimate values of the free energy changes involved in formation of the clathrin-associated protein complexes that comprise the coat. This model has been used to show how the binding of cargo might modify the coat parameters and thereby facilitate CCV formation. Recently, we have investigated the role that clathrin mediated endocytosis plays in the uptake of nanoparticles that are employed for drug delivery in order to establish criteria that might be used when optimizing their design. Experiments show that the uptake of nanoparticles is strongly size dependent. In particular, there is an optimal size at which cellular uptake is highest. In addition, there is a maximum size beyond which uptake via clathrin-mediated endocytosis does not occur. Various published results indicate that these sizes seem to be independent of the type of cells, nanoparticles, and ligands. We have been able to show that these observations are consequences of the kinetics of protein coat formation during CCP production. A manuscript based on this work, Efficiency of Cellular Uptake of Nanoparticles via Receptor-Mediated Endocytosis, recently was submitted for review. Studies involving other applications of our basic model to questions of cell and tissue biology also have been initiated. We also completed an investigation of the way system variables such as clathrin rigidity, clathrin-clathrin interactions, intrinsic curvature of clathrin oligomers, and the presence of adaptors and other clathrin-binding proteins affect the propensity for clathrin baskets to form when total clathrin concentration is low enough that it is a limiting factor. Our mathematical theory, based on principles of statistical thermodynamics, predicts the existence of a critical clathrin concentration below which baskets and cages will not form and describes the dependence of this quantity on the aforementioned variables (M. Muthukumar and R. Nossal, J. Chem. Phys. 139:125004, 2013). An expansion of this work is underway to account for similar behavior at the surface of cell membranes. Other facets of our research deal with adapting physical methods such as dynamic light scattering, small angle neutron scattering, and atomic force spectroscopy to infer the physical properties of the biochemical entities involved in RME. Due to the unusual properties of clathrin (it forms a three-legged supramolecular unit called a 'triskelion'), our analysis usually requires that we develop new mathematical theories and computational algorithms to link experimental observables to underlying biomolecular structure. Recent work employed atomic force microscopy (AFM) and single molecule force spectroscopy (SMFS) to characterize intermolecular interactions and domains of clathrin triskelions and their suprmolecular assemblies. For individual triskelions, SMFS revealed a series of unfolding events associated with individual heavy chain alpha-helix hairpins containing ca. 30 amino acid residues. Cooperative unraveling of several hairpin domains up to the size of the known repeating motif of ca. 145 amino acid residues also was seen. We found that the clathrin lattices of reconstituted clathrin-AP180 coats are energetically easier to unravel than those of native CCVs. Studies of such clathrin assemblies expose weaker, but coordinated, clathrin-clathrin interactions that are indicative of the inter-leg associations essential for clathrin mediated endocytosis. We recently have been working on new AFM technology that enables assessment of the mechanical properties of single clathrin cages, and have been using this technique to examine how interactions of clathrin-binding proteins such as auxilin and Hsp70 affect the mechanical stability of the cages that form when clathrin is copolymerized with such materials. This work extends our previous study of the mechanical properties of clathrin-coated vesicles (A. J. Jin, K. Prasad, P. D. Smith, E. M. Lafer, and R. Nossal. Biophys. J. 90:3333-44, 2006). We also have collaborated in the development of a mathematical model to explore how differences in the average number of parasites (merozoites) released from malaria-infected blood cells can affect clinically-relevant outcomes such as parasite load and anemia. This model was incorporated into a study of the replication of parasites in erythrocytes obtained from patients demonstrating various types of hemoglobinopathies. Finally, we have been investigating putative temperature-dependent lipid phase transitions occurring in higher eukaryotes. It is well established that microorganisms adjust the lipid composition of their membranes in response to changes in the temperature at which they are grown. Moreover, investigations carried out over many years have demonstrated that whole lipid extracts from various organisms exhibit singular properties at those temperatures (see, e.g., A.J. Jin, M. Edidin, R. Nossal, and N.L Gershfeld. Biochemistry 38:13275-8, 1999). Recently we have examined reports of the temperature-dependent behaviors of the nerves of poikilotherms (non-temperature-regulating organisms) in biological models such as squids and frogs. Analysis of axonal response, based on appproximations to the classic Hodgkin-Huxley equations, suggest that observed changes in the resting and action potentials reflect mechanical coupling between voltage-switchable ion channels and the lipid structure of the plasma membranes of such organisms.